Distance between 2 planets

[Danik]

1. Basically it tells me that Mars has a mass of 8*10^23kg.Phobos, its closest moon, whips around planet in 7 hrs. How far from Mars is Phobos?

I got that m=8*10^23 and T= 7 hrs . I am pretty sure i need to find the radius.

my only problem is that I cant find the formula where i can figure out r by using mass and T.
What am i doin wrong? Whats the formula that i need?
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution

[gabbagabbahey]

Hi Danik, welcome to PF!:smile:


my only problem is that I cant find the formula where i can figure out r by using mass and T.


Physics isn't really about looking up formulas for every conceivable scenario and plugging in known quantities (And it wouldn't be very interesting if it were)...It's about discovering and applying a small set of more general formulas (or Laws) to whichever problem you are investigating.

What simple physical laws (e.g. Coulomb's Law) do you think are relevant to this problem?

[Danik]

well, my first guess was Fc= mv^2/r . that wont work because of Fc and v which is like double unknown. I tried puttin GmM/mv^2 and that didnt work also ... =/ I just cant seem to think of any of the laws that work

[gabbagabbahey]

well, my first guess was Fc= mv^2/r . that wont work because of Fc and v which is like double unknown. I tried puttin GmM/mv^2 and that didnt work also ... =/ I just cant seem to think of any of the laws that work

I assume you mean Fg=GmM/r^2 ?

If so, why not combine those two equations to get GmM/r^2=mv^2/r (this amounts to assuming that the orbit of the moon is approximately circular, and then saying that it's centripetal acceleration is caused by its gravitational attraction to Mars....both reasonable assumptions IMO)?

Now, is there some relationship between the period of a circular orbit and it's orbital speed?

[Danik]

your right, so if i do that then i should come up with r=GMT^2/4п (if im not mistaken).

what should i do with the T? should i keep it at 7 hrs or should i convert it to 420 min or 25,200 s?

If i keep the hrs then i should come up with 2.05*10^15 m

[jegues]

what should i do with the T? If i keep the hrs then i should come up with 2.05*10^15 m

If you want an answer in SI units (e.g. meters) then the components(e.g. G, M, T) in which you use to generate that answer need to be in SI units.

What's the SI unit for time, hours or seconds?

[Danik]

what do u mean?

[acr]

Can you say Kepler's 3rd?

[jegues]

what do u mean?

I'm assuming you are wanting an answer in meters. Meters is the SI unit for length. (SI units are a system of units used by the international scientific community.) So if you want to generate an answer that is in SI units the variables you use to generate it also have to be in SI units.

What's the standard unit for time?

[gabbagabbahey]

Can you say Kepler's 3rd?

There's more than one way to skin a cat :wink:

[Danik]

its in seconds. so the T is in 25,200 s